Question

Calculate dy/dx for the following:
(i) y(x) = cos[x^3exp(x)][ln(x)]^-1
(ii) y(x) = ln[ln(x^3)]

Answer 1

Apply product rule, chain rule, power rule, ...

Answer 2

have fun!

Answer 3

\(y(x) = \cos(x^3e^x) * (\ln(x))^{-1}\)

\(y'(x) = \cos(x^3e^x) * ((\ln(x))^{-1})' + (\cos(x^3e^x))' * (\ln(x))^{-1}\)

...

Answer 4

It may be simpler if you drop the ln(x) to the denominator and apply quotient rule instead.